Hi,
I have exchanged custom item for CPs not long ago, it has appeared in my inventory but it didn't spawn on my location (I am in a fighter) and there is no galactic position in "Manage owned items". Also no CPs were charged for it yet.
Any idea what is wrong?

Yeah, as Kyria said. the Custom items are automatically spawned, not like custom images which need to be approved first. However, these items are not spawned at your location until the art team have actually approved them, whereupon they will spawn.